# Properties

 Label 5445.2.a.ca Level $5445$ Weight $2$ Character orbit 5445.a Self dual yes Analytic conductor $43.479$ Analytic rank $1$ Dimension $8$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$5445 = 3^{2} \cdot 5 \cdot 11^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 5445.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$43.4785439006$$ Analytic rank: $$1$$ Dimension: $$8$$ Coefficient field: $$\mathbb{Q}[x]/(x^{8} - \cdots)$$ Defining polynomial: $$x^{8} - 4x^{7} - 3x^{6} + 22x^{5} - 3x^{4} - 32x^{3} + 9x^{2} + 8x + 1$$ x^8 - 4*x^7 - 3*x^6 + 22*x^5 - 3*x^4 - 32*x^3 + 9*x^2 + 8*x + 1 Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 495) Fricke sign: $$1$$ Sato-Tate group: $\mathrm{SU}(2)$

## $q$-expansion

Coefficients of the $$q$$-expansion are expressed in terms of a basis $$1,\beta_1,\ldots,\beta_{7}$$ for the coefficient ring described below. We also show the integral $$q$$-expansion of the trace form.

 $$f(q)$$ $$=$$ $$q + (\beta_1 - 1) q^{2} + (\beta_{7} + \beta_{6} - \beta_{3} - \beta_1) q^{4} - q^{5} + (\beta_{7} - \beta_{2} - \beta_1 + 1) q^{7} + ( - \beta_{7} - \beta_{6} + 2 \beta_{3} + \beta_{2} + \beta_1) q^{8}+O(q^{10})$$ q + (b1 - 1) * q^2 + (b7 + b6 - b3 - b1) * q^4 - q^5 + (b7 - b2 - b1 + 1) * q^7 + (-b7 - b6 + 2*b3 + b2 + b1) * q^8 $$q + (\beta_1 - 1) q^{2} + (\beta_{7} + \beta_{6} - \beta_{3} - \beta_1) q^{4} - q^{5} + (\beta_{7} - \beta_{2} - \beta_1 + 1) q^{7} + ( - \beta_{7} - \beta_{6} + 2 \beta_{3} + \beta_{2} + \beta_1) q^{8} + ( - \beta_1 + 1) q^{10} + ( - \beta_{7} - 2 \beta_{6} + 2 \beta_{5} + \beta_{3} + 2) q^{13} + ( - \beta_{5} - \beta_{4} + 2 \beta_1 - 3) q^{14} + (\beta_{6} + 2 \beta_{4} - 2 \beta_{3} - \beta_{2} - 2 \beta_1 + 2) q^{16} + (\beta_{7} + \beta_{6} - \beta_{5} + \beta_{4} - 2 \beta_{2} - \beta_1 - 1) q^{17} + ( - \beta_{7} + \beta_{6} + \beta_{3} + 2 \beta_{2} + \beta_1) q^{19} + ( - \beta_{7} - \beta_{6} + \beta_{3} + \beta_1) q^{20} + (\beta_{7} + \beta_{6} - 2 \beta_{5} - 2 \beta_{3} + \beta_{2} + \beta_1 - 2) q^{23} + q^{25} + (3 \beta_{6} - \beta_{5} + \beta_{4} - \beta_{3} - 1) q^{26} + (\beta_{6} + \beta_{4} - 2 \beta_{3} - 2 \beta_1 + 3) q^{28} + ( - 2 \beta_{7} - 2 \beta_{6} + \beta_{5} - \beta_{4} + 2 \beta_{3} - 1) q^{29} + ( - \beta_{7} - \beta_{6} + 2 \beta_{5} - \beta_{4} - \beta_{3} - \beta_1 + 1) q^{31} + ( - 2 \beta_{7} - 4 \beta_{6} + \beta_{5} - 5 \beta_{4} + 2 \beta_{3} + \beta_{2} + 3 \beta_1 - 4) q^{32} + ( - 3 \beta_{6} - 5 \beta_{4} + \beta_{2} - 1) q^{34} + ( - \beta_{7} + \beta_{2} + \beta_1 - 1) q^{35} + (\beta_{6} - \beta_{5} - 2 \beta_{4} + 2 \beta_{2} - \beta_1 - 2) q^{37} + (\beta_{7} + \beta_{6} + 2 \beta_{5} + 2 \beta_{4} - 2 \beta_{3} + \beta_{2} - \beta_1 + 2) q^{38} + (\beta_{7} + \beta_{6} - 2 \beta_{3} - \beta_{2} - \beta_1) q^{40} + ( - \beta_{7} - 3 \beta_{6} - \beta_{3} + 2 \beta_{2} + 2 \beta_1 - 2) q^{41} + (\beta_{7} + 3 \beta_{6} - 2 \beta_{5} + 3 \beta_{4} - 3 \beta_{3} - 2 \beta_{2} + 2 \beta_1 - 1) q^{43} + ( - \beta_{6} + 2 \beta_{4} + 2 \beta_{3} - \beta_{2} + 2) q^{46} + ( - \beta_{7} + \beta_{6} - \beta_{4} - 2 \beta_{3} - 3) q^{47} + (\beta_{7} - 2 \beta_{6} + 2 \beta_{4} + \beta_{3} - 3 \beta_{2} - \beta_1 + 2) q^{49} + (\beta_1 - 1) q^{50} + (\beta_{7} - \beta_{6} - \beta_{5} - 4 \beta_{4} + 3 \beta_{2} + 2 \beta_1 - 3) q^{52} + ( - 4 \beta_{7} - 2 \beta_{6} + \beta_{5} + 2 \beta_{3} + 2 \beta_{2} - \beta_1 + 6) q^{53} + ( - 4 \beta_{7} - 5 \beta_{6} + 3 \beta_{5} + 6 \beta_{3} + 2 \beta_{2} + 2 \beta_1 + 1) q^{56} + (\beta_{6} + \beta_{4} - 2 \beta_{3} - 2 \beta_{2} - 6 \beta_1 + 3) q^{58} + (\beta_{7} + 2 \beta_{6} - \beta_{4} - \beta_{3} - 2 \beta_{2} + 2 \beta_1 - 4) q^{59} + (\beta_{7} + \beta_{6} - 2 \beta_{5} - 5 \beta_{4} + \beta_{3} + 2 \beta_{2} + \beta_1 - 4) q^{61} + ( - 3 \beta_{7} - \beta_{6} + \beta_{4} + 4 \beta_{3} + 2 \beta_1 - 1) q^{62} + (3 \beta_{7} + 5 \beta_{6} - 2 \beta_{5} + 5 \beta_{4} - \beta_{3} - 6 \beta_{2} - 7 \beta_1 + 5) q^{64} + (\beta_{7} + 2 \beta_{6} - 2 \beta_{5} - \beta_{3} - 2) q^{65} + (\beta_{7} + 4 \beta_{6} - 2 \beta_{4} - \beta_{3} + 2 \beta_{2} - 2) q^{67} + ( - 2 \beta_{7} + 2 \beta_{6} - \beta_{5} + 8 \beta_{4} - 4 \beta_{2} - 2 \beta_1 + 3) q^{68} + (\beta_{5} + \beta_{4} - 2 \beta_1 + 3) q^{70} + (2 \beta_{6} - 3 \beta_{5} + 6 \beta_{4} + \beta_{3} + 2 \beta_{2} - 2 \beta_1 + 5) q^{71} + ( - 3 \beta_{7} - \beta_{6} + \beta_{4} + 2 \beta_{3} - \beta_{2} - 3 \beta_1 + 6) q^{73} + ( - \beta_{7} - \beta_{6} + \beta_{5} + 5 \beta_{4} + \beta_{3} - 2 \beta_{2} - 2 \beta_1 + 1) q^{74} + ( - \beta_{6} + 2 \beta_{3} + \beta_{2} + 6 \beta_1 - 4) q^{76} + ( - 4 \beta_{5} + \beta_{4} - 2 \beta_{3} - 2 \beta_{2} + 4 \beta_1 - 4) q^{79} + ( - \beta_{6} - 2 \beta_{4} + 2 \beta_{3} + \beta_{2} + 2 \beta_1 - 2) q^{80} + (4 \beta_{6} - 2 \beta_{5} + 6 \beta_{4} + \beta_{3} - 3 \beta_{2} - 5 \beta_1 + 5) q^{82} + (2 \beta_{6} + 4 \beta_{5} - \beta_{4} - 2 \beta_{3} - \beta_{2} - \beta_1 - 9) q^{83} + ( - \beta_{7} - \beta_{6} + \beta_{5} - \beta_{4} + 2 \beta_{2} + \beta_1 + 1) q^{85} + ( - 6 \beta_{6} + 2 \beta_{5} - 9 \beta_{4} + 3 \beta_{3} + 4 \beta_{2} + 4 \beta_1 + 2) q^{86} + ( - \beta_{6} + \beta_{5} - 4 \beta_{4} - 2 \beta_{3} + 2 \beta_{2} - 7) q^{89} + ( - \beta_{7} - 4 \beta_{6} + 2 \beta_{5} + 2 \beta_{4} + 5 \beta_{3} + \beta_{2} - 3 \beta_1 + 8) q^{91} + (3 \beta_{5} - 3 \beta_{4} - \beta_{2} - 3 \beta_1 + 2) q^{92} + ( - 3 \beta_{7} - 5 \beta_{6} + 2 \beta_{5} - \beta_{4} + 5 \beta_{3} - \beta_1 + 4) q^{94} + (\beta_{7} - \beta_{6} - \beta_{3} - 2 \beta_{2} - \beta_1) q^{95} + ( - 3 \beta_{6} - 3 \beta_{5} - 2 \beta_{4} + \beta_{3} + 3 \beta_{2} + 2 \beta_1 + 1) q^{97} + (\beta_{7} + \beta_{6} - 3 \beta_{5} - 5 \beta_{4} - 2 \beta_{3} - 4) q^{98}+O(q^{100})$$ q + (b1 - 1) * q^2 + (b7 + b6 - b3 - b1) * q^4 - q^5 + (b7 - b2 - b1 + 1) * q^7 + (-b7 - b6 + 2*b3 + b2 + b1) * q^8 + (-b1 + 1) * q^10 + (-b7 - 2*b6 + 2*b5 + b3 + 2) * q^13 + (-b5 - b4 + 2*b1 - 3) * q^14 + (b6 + 2*b4 - 2*b3 - b2 - 2*b1 + 2) * q^16 + (b7 + b6 - b5 + b4 - 2*b2 - b1 - 1) * q^17 + (-b7 + b6 + b3 + 2*b2 + b1) * q^19 + (-b7 - b6 + b3 + b1) * q^20 + (b7 + b6 - 2*b5 - 2*b3 + b2 + b1 - 2) * q^23 + q^25 + (3*b6 - b5 + b4 - b3 - 1) * q^26 + (b6 + b4 - 2*b3 - 2*b1 + 3) * q^28 + (-2*b7 - 2*b6 + b5 - b4 + 2*b3 - 1) * q^29 + (-b7 - b6 + 2*b5 - b4 - b3 - b1 + 1) * q^31 + (-2*b7 - 4*b6 + b5 - 5*b4 + 2*b3 + b2 + 3*b1 - 4) * q^32 + (-3*b6 - 5*b4 + b2 - 1) * q^34 + (-b7 + b2 + b1 - 1) * q^35 + (b6 - b5 - 2*b4 + 2*b2 - b1 - 2) * q^37 + (b7 + b6 + 2*b5 + 2*b4 - 2*b3 + b2 - b1 + 2) * q^38 + (b7 + b6 - 2*b3 - b2 - b1) * q^40 + (-b7 - 3*b6 - b3 + 2*b2 + 2*b1 - 2) * q^41 + (b7 + 3*b6 - 2*b5 + 3*b4 - 3*b3 - 2*b2 + 2*b1 - 1) * q^43 + (-b6 + 2*b4 + 2*b3 - b2 + 2) * q^46 + (-b7 + b6 - b4 - 2*b3 - 3) * q^47 + (b7 - 2*b6 + 2*b4 + b3 - 3*b2 - b1 + 2) * q^49 + (b1 - 1) * q^50 + (b7 - b6 - b5 - 4*b4 + 3*b2 + 2*b1 - 3) * q^52 + (-4*b7 - 2*b6 + b5 + 2*b3 + 2*b2 - b1 + 6) * q^53 + (-4*b7 - 5*b6 + 3*b5 + 6*b3 + 2*b2 + 2*b1 + 1) * q^56 + (b6 + b4 - 2*b3 - 2*b2 - 6*b1 + 3) * q^58 + (b7 + 2*b6 - b4 - b3 - 2*b2 + 2*b1 - 4) * q^59 + (b7 + b6 - 2*b5 - 5*b4 + b3 + 2*b2 + b1 - 4) * q^61 + (-3*b7 - b6 + b4 + 4*b3 + 2*b1 - 1) * q^62 + (3*b7 + 5*b6 - 2*b5 + 5*b4 - b3 - 6*b2 - 7*b1 + 5) * q^64 + (b7 + 2*b6 - 2*b5 - b3 - 2) * q^65 + (b7 + 4*b6 - 2*b4 - b3 + 2*b2 - 2) * q^67 + (-2*b7 + 2*b6 - b5 + 8*b4 - 4*b2 - 2*b1 + 3) * q^68 + (b5 + b4 - 2*b1 + 3) * q^70 + (2*b6 - 3*b5 + 6*b4 + b3 + 2*b2 - 2*b1 + 5) * q^71 + (-3*b7 - b6 + b4 + 2*b3 - b2 - 3*b1 + 6) * q^73 + (-b7 - b6 + b5 + 5*b4 + b3 - 2*b2 - 2*b1 + 1) * q^74 + (-b6 + 2*b3 + b2 + 6*b1 - 4) * q^76 + (-4*b5 + b4 - 2*b3 - 2*b2 + 4*b1 - 4) * q^79 + (-b6 - 2*b4 + 2*b3 + b2 + 2*b1 - 2) * q^80 + (4*b6 - 2*b5 + 6*b4 + b3 - 3*b2 - 5*b1 + 5) * q^82 + (2*b6 + 4*b5 - b4 - 2*b3 - b2 - b1 - 9) * q^83 + (-b7 - b6 + b5 - b4 + 2*b2 + b1 + 1) * q^85 + (-6*b6 + 2*b5 - 9*b4 + 3*b3 + 4*b2 + 4*b1 + 2) * q^86 + (-b6 + b5 - 4*b4 - 2*b3 + 2*b2 - 7) * q^89 + (-b7 - 4*b6 + 2*b5 + 2*b4 + 5*b3 + b2 - 3*b1 + 8) * q^91 + (3*b5 - 3*b4 - b2 - 3*b1 + 2) * q^92 + (-3*b7 - 5*b6 + 2*b5 - b4 + 5*b3 - b1 + 4) * q^94 + (b7 - b6 - b3 - 2*b2 - b1) * q^95 + (-3*b6 - 3*b5 - 2*b4 + b3 + 3*b2 + 2*b1 + 1) * q^97 + (b7 + b6 - 3*b5 - 5*b4 - 2*b3 - 4) * q^98 $$\operatorname{Tr}(f)(q)$$ $$=$$ $$8 q - 4 q^{2} + 6 q^{4} - 8 q^{5} + 8 q^{7} - 12 q^{8}+O(q^{10})$$ 8 * q - 4 * q^2 + 6 * q^4 - 8 * q^5 + 8 * q^7 - 12 * q^8 $$8 q - 4 q^{2} + 6 q^{4} - 8 q^{5} + 8 q^{7} - 12 q^{8} + 4 q^{10} + 6 q^{13} - 14 q^{14} + 14 q^{16} - 8 q^{17} - 2 q^{19} - 6 q^{20} - 4 q^{23} + 8 q^{25} + 2 q^{26} + 24 q^{28} - 22 q^{29} + 10 q^{31} - 28 q^{32} - 2 q^{34} - 8 q^{35} - 14 q^{37} + 20 q^{38} + 12 q^{40} - 22 q^{41} + 14 q^{43} - 2 q^{46} - 10 q^{47} - 4 q^{50} - 10 q^{52} + 18 q^{53} - 34 q^{56} + 12 q^{58} - 2 q^{59} - 14 q^{61} - 30 q^{62} + 30 q^{64} - 6 q^{65} + 10 q^{67} - 6 q^{68} + 14 q^{70} + 2 q^{71} + 16 q^{73} - 24 q^{74} - 22 q^{76} - 16 q^{79} - 14 q^{80} + 10 q^{82} - 46 q^{83} + 8 q^{85} + 28 q^{86} - 38 q^{89} + 8 q^{91} + 24 q^{92} - 10 q^{94} + 2 q^{95} - 4 q^{97} - 4 q^{98}+O(q^{100})$$ 8 * q - 4 * q^2 + 6 * q^4 - 8 * q^5 + 8 * q^7 - 12 * q^8 + 4 * q^10 + 6 * q^13 - 14 * q^14 + 14 * q^16 - 8 * q^17 - 2 * q^19 - 6 * q^20 - 4 * q^23 + 8 * q^25 + 2 * q^26 + 24 * q^28 - 22 * q^29 + 10 * q^31 - 28 * q^32 - 2 * q^34 - 8 * q^35 - 14 * q^37 + 20 * q^38 + 12 * q^40 - 22 * q^41 + 14 * q^43 - 2 * q^46 - 10 * q^47 - 4 * q^50 - 10 * q^52 + 18 * q^53 - 34 * q^56 + 12 * q^58 - 2 * q^59 - 14 * q^61 - 30 * q^62 + 30 * q^64 - 6 * q^65 + 10 * q^67 - 6 * q^68 + 14 * q^70 + 2 * q^71 + 16 * q^73 - 24 * q^74 - 22 * q^76 - 16 * q^79 - 14 * q^80 + 10 * q^82 - 46 * q^83 + 8 * q^85 + 28 * q^86 - 38 * q^89 + 8 * q^91 + 24 * q^92 - 10 * q^94 + 2 * q^95 - 4 * q^97 - 4 * q^98

Basis of coefficient ring in terms of a root $$\nu$$ of $$x^{8} - 4x^{7} - 3x^{6} + 22x^{5} - 3x^{4} - 32x^{3} + 9x^{2} + 8x + 1$$ :

 $$\beta_{1}$$ $$=$$ $$\nu$$ v $$\beta_{2}$$ $$=$$ $$-\nu^{7} + 4\nu^{6} + 3\nu^{5} - 22\nu^{4} + 4\nu^{3} + 30\nu^{2} - 13\nu - 4$$ -v^7 + 4*v^6 + 3*v^5 - 22*v^4 + 4*v^3 + 30*v^2 - 13*v - 4 $$\beta_{3}$$ $$=$$ $$\nu^{7} - 4\nu^{6} - 3\nu^{5} + 22\nu^{4} - 3\nu^{3} - 32\nu^{2} + 10\nu + 6$$ v^7 - 4*v^6 - 3*v^5 + 22*v^4 - 3*v^3 - 32*v^2 + 10*v + 6 $$\beta_{4}$$ $$=$$ $$4\nu^{7} - 17\nu^{6} - 8\nu^{5} + 91\nu^{4} - 34\nu^{3} - 124\nu^{2} + 66\nu + 19$$ 4*v^7 - 17*v^6 - 8*v^5 + 91*v^4 - 34*v^3 - 124*v^2 + 66*v + 19 $$\beta_{5}$$ $$=$$ $$7\nu^{7} - 29\nu^{6} - 16\nu^{5} + 154\nu^{4} - 48\nu^{3} - 206\nu^{2} + 101\nu + 30$$ 7*v^7 - 29*v^6 - 16*v^5 + 154*v^4 - 48*v^3 - 206*v^2 + 101*v + 30 $$\beta_{6}$$ $$=$$ $$-7\nu^{7} + 30\nu^{6} + 13\nu^{5} - 159\nu^{4} + 62\nu^{3} + 214\nu^{2} - 115\nu - 33$$ -7*v^7 + 30*v^6 + 13*v^5 - 159*v^4 + 62*v^3 + 214*v^2 - 115*v - 33 $$\beta_{7}$$ $$=$$ $$8\nu^{7} - 34\nu^{6} - 16\nu^{5} + 181\nu^{4} - 65\nu^{3} - 245\nu^{2} + 124\nu + 38$$ 8*v^7 - 34*v^6 - 16*v^5 + 181*v^4 - 65*v^3 - 245*v^2 + 124*v + 38
 $$\nu$$ $$=$$ $$\beta_1$$ b1 $$\nu^{2}$$ $$=$$ $$\beta_{7} + \beta_{6} - \beta_{3} + \beta _1 + 1$$ b7 + b6 - b3 + b1 + 1 $$\nu^{3}$$ $$=$$ $$2\beta_{7} + 2\beta_{6} - \beta_{3} + \beta_{2} + 5\beta_1$$ 2*b7 + 2*b6 - b3 + b2 + 5*b1 $$\nu^{4}$$ $$=$$ $$8\beta_{7} + 9\beta_{6} + 2\beta_{4} - 6\beta_{3} + 3\beta_{2} + 10\beta _1 + 3$$ 8*b7 + 9*b6 + 2*b4 - 6*b3 + 3*b2 + 10*b1 + 3 $$\nu^{5}$$ $$=$$ $$20\beta_{7} + 23\beta_{6} + \beta_{5} + 5\beta_{4} - 12\beta_{3} + 14\beta_{2} + 36\beta _1 + 2$$ 20*b7 + 23*b6 + b5 + 5*b4 - 12*b3 + 14*b2 + 36*b1 + 2 $$\nu^{6}$$ $$=$$ $$64\beta_{7} + 79\beta_{6} + 4\beta_{5} + 25\beta_{4} - 44\beta_{3} + 43\beta_{2} + 94\beta _1 + 16$$ 64*b7 + 79*b6 + 4*b5 + 25*b4 - 44*b3 + 43*b2 + 94*b1 + 16 $$\nu^{7}$$ $$=$$ $$178\beta_{7} + 225\beta_{6} + 19\beta_{5} + 71\beta_{4} - 114\beta_{3} + 151\beta_{2} + 301\beta _1 + 30$$ 178*b7 + 225*b6 + 19*b5 + 71*b4 - 114*b3 + 151*b2 + 301*b1 + 30

## Embeddings

For each embedding $$\iota_m$$ of the coefficient field, the values $$\iota_m(a_n)$$ are shown below.

For more information on an embedded modular form you can click on its label.

Label $$\iota_m(\nu)$$ $$a_{2}$$ $$a_{3}$$ $$a_{4}$$ $$a_{5}$$ $$a_{6}$$ $$a_{7}$$ $$a_{8}$$ $$a_{9}$$ $$a_{10}$$
1.1
 −1.75229 −1.39491 −0.226007 −0.205878 0.909121 1.48523 2.13569 3.04904
−2.75229 0 5.57509 −1.00000 0 2.73187 −9.83966 0 2.75229
1.2 −2.39491 0 3.73560 −1.00000 0 1.96984 −4.15660 0 2.39491
1.3 −1.22601 0 −0.496906 −1.00000 0 −0.451695 3.06123 0 1.22601
1.4 −1.20588 0 −0.545859 −1.00000 0 4.31539 3.06999 0 1.20588
1.5 −0.0908791 0 −1.99174 −1.00000 0 −2.45732 0.362766 0 0.0908791
1.6 0.485227 0 −1.76455 −1.00000 0 −1.61947 −1.82666 0 −0.485227
1.7 1.13569 0 −0.710206 −1.00000 0 4.10132 −3.07796 0 −1.13569
1.8 2.04904 0 2.19858 −1.00000 0 −0.589936 0.406903 0 −2.04904
 $$n$$: e.g. 2-40 or 990-1000 Embeddings: e.g. 1-3 or 1.8 Significant digits: Format: Complex embeddings Normalized embeddings Satake parameters Satake angles

## Atkin-Lehner signs

$$p$$ Sign
$$3$$ $$1$$
$$5$$ $$1$$
$$11$$ $$1$$

## Inner twists

This newform does not admit any (nontrivial) inner twists.

## Twists

By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 5445.2.a.ca 8
3.b odd 2 1 5445.2.a.cd 8
11.b odd 2 1 5445.2.a.cc 8
11.c even 5 2 495.2.n.h yes 16
33.d even 2 1 5445.2.a.cb 8
33.h odd 10 2 495.2.n.g 16

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
495.2.n.g 16 33.h odd 10 2
495.2.n.h yes 16 11.c even 5 2
5445.2.a.ca 8 1.a even 1 1 trivial
5445.2.a.cb 8 33.d even 2 1
5445.2.a.cc 8 11.b odd 2 1
5445.2.a.cd 8 3.b odd 2 1

## Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $$S_{2}^{\mathrm{new}}(\Gamma_0(5445))$$:

 $$T_{2}^{8} + 4T_{2}^{7} - 3T_{2}^{6} - 24T_{2}^{5} - 8T_{2}^{4} + 32T_{2}^{3} + 14T_{2}^{2} - 10T_{2} - 1$$ T2^8 + 4*T2^7 - 3*T2^6 - 24*T2^5 - 8*T2^4 + 32*T2^3 + 14*T2^2 - 10*T2 - 1 $$T_{7}^{8} - 8T_{7}^{7} + 4T_{7}^{6} + 86T_{7}^{5} - 98T_{7}^{4} - 290T_{7}^{3} + 203T_{7}^{2} + 362T_{7} + 101$$ T7^8 - 8*T7^7 + 4*T7^6 + 86*T7^5 - 98*T7^4 - 290*T7^3 + 203*T7^2 + 362*T7 + 101 $$T_{23}^{8} + 4T_{23}^{7} - 65T_{23}^{6} - 46T_{23}^{5} + 1309T_{23}^{4} - 3042T_{23}^{3} + 2139T_{23}^{2} - 144T_{23} - 1$$ T23^8 + 4*T23^7 - 65*T23^6 - 46*T23^5 + 1309*T23^4 - 3042*T23^3 + 2139*T23^2 - 144*T23 - 1 $$T_{53}^{8} - 18 T_{53}^{7} - 74 T_{53}^{6} + 2934 T_{53}^{5} - 10906 T_{53}^{4} - 75540 T_{53}^{3} + 547489 T_{53}^{2} - 996010 T_{53} + 392695$$ T53^8 - 18*T53^7 - 74*T53^6 + 2934*T53^5 - 10906*T53^4 - 75540*T53^3 + 547489*T53^2 - 996010*T53 + 392695

## Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ $$T^{8} + 4 T^{7} - 3 T^{6} - 24 T^{5} + \cdots - 1$$
$3$ $$T^{8}$$
$5$ $$(T + 1)^{8}$$
$7$ $$T^{8} - 8 T^{7} + 4 T^{6} + 86 T^{5} + \cdots + 101$$
$11$ $$T^{8}$$
$13$ $$T^{8} - 6 T^{7} - 37 T^{6} + \cdots - 1331$$
$17$ $$T^{8} + 8 T^{7} - 34 T^{6} + \cdots + 4231$$
$19$ $$T^{8} + 2 T^{7} - 91 T^{6} + \cdots + 5929$$
$23$ $$T^{8} + 4 T^{7} - 65 T^{6} - 46 T^{5} + \cdots - 1$$
$29$ $$T^{8} + 22 T^{7} + 145 T^{6} + \cdots + 1891$$
$31$ $$T^{8} - 10 T^{7} - 61 T^{6} + \cdots + 23081$$
$37$ $$T^{8} + 14 T^{7} - 3 T^{6} + \cdots + 122881$$
$41$ $$T^{8} + 22 T^{7} + 36 T^{6} + \cdots + 2647555$$
$43$ $$T^{8} - 14 T^{7} - 172 T^{6} + \cdots - 2417279$$
$47$ $$T^{8} + 10 T^{7} - 96 T^{6} + \cdots - 589$$
$53$ $$T^{8} - 18 T^{7} - 74 T^{6} + \cdots + 392695$$
$59$ $$T^{8} + 2 T^{7} - 173 T^{6} + \cdots - 88469$$
$61$ $$T^{8} + 14 T^{7} - 159 T^{6} + \cdots - 462499$$
$67$ $$T^{8} - 10 T^{7} - 173 T^{6} + \cdots - 597971$$
$71$ $$T^{8} - 2 T^{7} - 399 T^{6} + \cdots - 9049805$$
$73$ $$T^{8} - 16 T^{7} - 157 T^{6} + \cdots - 3045251$$
$79$ $$T^{8} + 16 T^{7} - 342 T^{6} + \cdots + 5735705$$
$83$ $$T^{8} + 46 T^{7} + 535 T^{6} + \cdots - 41467789$$
$89$ $$T^{8} + 38 T^{7} + 438 T^{6} + \cdots - 5696725$$
$97$ $$T^{8} + 4 T^{7} - 404 T^{6} + \cdots - 7598959$$